Sometimes I find that even if you "know" depth of field it pays to take a few experiment shots at other apertures when you've a scene where the subject isn't moving much (I'm assuming the snake was fairly still). Even LCD review can give some idea how things are going, and at the very least you get a few usable options which might give you a better shot than your original aperture selection.
Well just a guess here mind you, but my guess is this is actually a combo of two factors, a narrow DOF and also it looks to me like your picking up some reflection most likely from a pexiglass window as well which is having an effect on the detail of that first coil. So an increase in DOF would help perhaps to a certain extent, but really getting your lens closer to the window (to the point where the hood is touching) or repositioning to one side or the other and moving say up or down just a tad to change the angle will often allow you to push a lot of that reflection to the side and then weed it out in post.